Manipulation complexity and gender neutrality in stable marriage procedures Maria Silvia Pini Francesca Rossi Email author K. Brent Venable Toby Walsh Article

First Online: 07 February 2010 DOI :
10.1007/s10458-010-9121-x

Cite this article as: Pini, M.S., Rossi, F., Venable, K.B. et al. Auton Agent Multi-Agent Syst (2011) 22: 183. doi:10.1007/s10458-010-9121-x Abstract The stable marriage problem is a well-known problem of matching men to women so that no man and woman who are not married to each other both prefer each other. Such a problem has a wide variety of practical applications, ranging from matching resident doctors, to hospitals to matching students to schools. A well-known algorithm to solve this problem is the Gale–Shapley algorithm, which runs in quadratic time in the number of men/women. It has been proven that stable marriage procedures can always be manipulated. Whilst the Gale–Shapley algorithm is computationally easy to manipulate, we prove that there exist stable marriage procedures which are NP-hard to manipulate. We also consider the relationship between voting theory and stable marriage procedures, showing that voting rules which are NP-hard to manipulate can be used to define stable marriage procedures which are themselves NP-hard to manipulate. Finally, we consider the issue that stable marriage procedures like Gale–Shapley favour one gender over the other, and we show how to use voting rules to make any stable marriage procedure gender neutral.

Keywords Computational social choice Stable marriage problems Manipulation Voting theory

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MATH CrossRef MathSciNet Authors and Affiliations Maria Silvia Pini Francesca Rossi Email author K. Brent Venable Toby Walsh 1. Dipartimento di Matematica Pura ed Applicata Università di Padova Padua Italy 2. NICTA and UNSW Sydney Australia